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Dissertation/Thesis Abstract

Dynamics of Predator-Prey Models with Ratio-Dependent Functional Response and Diffusion
by Cervantes Casiano, Ricardo, M.S., University of South Dakota, 2016, 96; 10131446
Abstract (Summary)

One of the reasons why predation is important is that no organism can live, grow, and reproduce without consuming resources. We have studied possible scenarios of pattern formation in three different predator-prey models; the Rozenweig-McArthur, and the Leslie-Gower model with alternative food for the predator with different functional responses; one uses a prey-dependent functional response while the other use ratio-dependent functional response. The Turing patterns observed for the Leslie-Gower model with prey dependence are of two types, hot spot patterns and cold spot patterns while the ratio dependent model exhibit only hot spot patterns. Also, the labyrinthine pattern is also observed for some choices of parameters values within the Turing-Hopf domain for both models.

Indexing (document details)
Advisor: Flores, Jose D., Jiang, Nan
Commitee: Keller, Christina
School: University of South Dakota
Department: Mathematics
School Location: United States -- South Dakota
Source: MAI 55/06M(E), Masters Abstracts International
Subjects: Applied Mathematics
Keywords: Applied mathematics, Hopf bifurcation, Pattern formation, Predator prey models, Reaction diffusion, Turing instabilities
Publication Number: 10131446
ISBN: 978-1-339-89239-9
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